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Finding the Third Proportional to 412.75 and 681.38

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Solution

The third proportional to 412.75 and 681.38 is: 1,124.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.75 : 681.38 = 681.38 : x
  2. Step 2: Convert to fraction form
    412.75/681.38 = 681.38/x
  3. Step 3: Cross multiply
    412.75x = 681.38 × 681.38
  4. Step 4: Simplify right side
    412.75x = 464,271.89
  5. Step 5: Solve for x
    x = 464,271.89/412.75
  6. Step 6: Final answer
    x = 1,124.83

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.